{
 "cells": [
  {
   "cell_type": "markdown",
   "source": [
    "## 激活函数及可视化"
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "---"
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "#### 介绍"
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "激活函数是深度学习中很重要的一个概念。在神经网络中，我们经常使用线性运算来解决线性问题。但是日常生活中的大多数问题，都不是简单的线性运算。为此，我们引入了激活函数来解决非线性的问题。本实验主要讲解了深度学习中常用的激活函数的各种形式以及如何利用 PyTorch 对其进行实现。最后利用学到的激活函数，建立了一个简单的三层神经网络模型。"
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "#### 知识点"
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "- Sigmoid 函数\n",
    "- ReLU 函数\n",
    "- Tanh 函数"
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "---"
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "### 激活函数"
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "激活函数是深度学习中一个很重要的概念。在神经网络中，我们经常使用线性运算来解决线性问题。但是日常生活中的大多数问题，都不是简单的线性问题。为此，我们引入了激活函数来解决非线性的问题。"
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "简单的说，传统的全连接网络就是让数据不断的通过线性函数层和激活函数层，进而得到最终的预测结果。因此，如果我们学习完激活函数后，就可以结合之前学过的线性函数来完成一个传统的全连接网络模型了。"
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "常见的激活函数有 Sigmoid 函数（又名 Logistic 函数）、tanh 函数（又名双曲正切函数），ReLU 函数（又名线性修正单元函数）等。"
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "#### Sigmoid 函数"
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "Sigmoid 函数是深度学习发展中最经典的且最先被使用的激活函数之一。它的公式如下所示："
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "$$\\sigma(z) = \\frac{1}{1+e^{-z}}$$"
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "其中 $z$ 表示函数的输入，$\\sigma$ 表示函数的输出。根据公式，我们可以画出相关的几何图像："
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "source": [
    "import numpy as np\r\n",
    "import matplotlib.pyplot as plt\r\n",
    "%matplotlib inline\r\n",
    "\r\n",
    "# 手写 sigmoid 函数\r\n",
    "def sigmoid(x): return 1 / (1 + np.exp(-x))\r\n",
    "\r\n",
    "# 画图\r\n",
    "y = np.linspace(-10, 10, 100)\r\n",
    "plt.plot(y, sigmoid(y), 'b')\r\n",
    "plt.grid(linestyle='--')\r\n",
    "plt.xticks([-4, -3, -2, -1, 0, 1, 2, 3, 4])\r\n",
    "plt.yticks([0, 0.5, 1])\r\n",
    "plt.ylim(0, 1)\r\n",
    "plt.xlim(-4, 4)\r\n",
    "plt.show()"
   ],
   "outputs": [
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"
     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "source": [
    "import numpy as np\r\n",
    "import matplotlib.pyplot as plt\r\n",
    "import seaborn as sns\r\n",
    "%matplotlib inline\r\n",
    "\r\n",
    "# sigmoid\r\n",
    "def sigmoid(x):\r\n",
    "    return 1/(1+np.exp(-x))\r\n",
    "# 画图\r\n",
    "x = np.linspace(-10,10,100)\r\n",
    "y = sigmoid(x)\r\n",
    "sns.set()\r\n",
    "sns.lineplot(x,y)\r\n",
    "# 利用sns画图真的很省心"
   ],
   "outputs": [
    {
     "output_type": "stream",
     "name": "stderr",
     "text": [
      "C:\\Users\\22459\\Miniconda3\\envs\\pytorch\\lib\\site-packages\\seaborn\\_decorators.py:36: FutureWarning: Pass the following variables as keyword args: x, y. From version 0.12, the only valid positional argument will be `data`, and passing other arguments without an explicit keyword will result in an error or misinterpretation.\n",
      "  warnings.warn(\n"
     ]
    },
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": [
       "<AxesSubplot:>"
      ]
     },
     "metadata": {},
     "execution_count": 13
    },
    {
     "output_type": "display_data",
     "data": {
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ],
      "image/svg+xml": "<?xml version=\"1.0\" encoding=\"utf-8\" standalone=\"no\"?>\r\n<!DOCTYPE svg PUBLIC \"-//W3C//DTD SVG 1.1//EN\"\r\n  \"http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd\">\r\n<svg height=\"251.399844pt\" version=\"1.1\" viewBox=\"0 0 373.99 251.399844\" width=\"373.99pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\">\r\n <metadata>\r\n  <rdf:RDF xmlns:cc=\"http://creativecommons.org/ns#\" xmlns:dc=\"http://purl.org/dc/elements/1.1/\" xmlns:rdf=\"http://www.w3.org/1999/02/22-rdf-syntax-ns#\">\r\n   <cc:Work>\r\n    <dc:type rdf:resource=\"http://purl.org/dc/dcmitype/StillImage\"/>\r\n    <dc:date>2021-08-13T10:14:48.950006</dc:date>\r\n    <dc:format>image/svg+xml</dc:format>\r\n    <dc:creator>\r\n     <cc:Agent>\r\n      <dc:title>Matplotlib v3.4.2, https://matplotlib.org/</dc:title>\r\n     </cc:Agent>\r\n    </dc:creator>\r\n   </cc:Work>\r\n  </rdf:RDF>\r\n </metadata>\r\n <defs>\r\n  <style 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"
     },
     "metadata": {}
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "从图中可以看到，激活函数 Sigmoid 在定义域内处处可导。但是，通过曲线的斜率，可以发现，当输入一个较小或较大的数时，该函数的导数会变得很小，梯度趋近于 0 。 举个例子，每一次的梯度值都减少 0.25，如果神经网络的隐含层过多，那么当梯度穿过多层后将变得非常接近于 0（可以理解为 0.5 的 n 次方），即出现梯度消失的现象，进而造成模型无法收敛。这也就是为什么，曾经被广泛使用的 Sigmoid 函数，现在却消声觅迹的原因。"
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "除了自定义 Sigmoid 函数之外，我们还可以通过 PyTorch 对其进行定义："
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "source": [
    "import torch\r\n",
    "import torch.nn as nn\r\n",
    "import torch.nn.functional as F\r\n",
    "\r\n",
    "# pytorch 中有两种实现方法\r\n",
    "x = torch.tensor([-1.0, 1.0, 2.0, 3.0])\r\n",
    "output = torch.sigmoid(x)\r\n",
    "print(output)\r\n",
    "s = nn.Sigmoid()\r\n",
    "output = s(x)\r\n",
    "print(output)"
   ],
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "tensor([0.2689, 0.7311, 0.8808, 0.9526])\n",
      "tensor([0.2689, 0.7311, 0.8808, 0.9526])\n"
     ]
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "source": [
    "# 不采用sigmoid的原因是因为当x极大或者极小(负数)的时候，通过sigmoid后值会趋近于1或-1\r\n",
    "# 使得曲线变得十分平缓，这使得梯度很小，如果多次通过sigmoid会造成梯度趋近于0的情况，产生“梯度消失”\r\n",
    "import torch\r\n",
    "import torch.nn as nn\r\n",
    "import torch.nn.functional as F\r\n",
    "\r\n",
    "# 在pytorch中torch和nn里面都要sigmoid\r\n",
    "x = torch.linspace(-10,10,1)\r\n",
    "print('torch.sigmoid',torch.sigmoid(x))\r\n",
    "s = nn.Sigmoid()\r\n",
    "y = s(x)\r\n",
    "print('nn.sigmoid',y)\r\n",
    "# torch.sigmoid()和nn.Sigmoid()一个是函数另一个是层的对象"
   ],
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "torch.sigmoid tensor([4.5398e-05])\n",
      "nn.sigmoid tensor([4.5398e-05])\n"
     ]
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "#### Tanh  函数"
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "Tanh 是双曲函数中的双曲正切函数。在数学中，双曲正切函数都是由双曲正弦函数和双曲余弦函数推导而来。函数的具体形式如下："
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "$$tanh(x)=\\frac{e^x-e^{-x}}{e^x+e^{-x}}$$"
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "Tanh 的函数图像如下:"
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "source": [
    "def tanh(x): return 2*sigmoid(2*x)-1\r\n",
    "\r\n",
    "\r\n",
    "y = np.linspace(-10, 10, 100)\r\n",
    "plt.plot(y, tanh(y), 'b')\r\n",
    "plt.grid(linestyle='--')\r\n",
    "plt.xlabel('X Axis')\r\n",
    "plt.ylabel('Y Axis')\r\n",
    "plt.xticks([-4, -3, -2, -1, 0, 1, 2, 3, 4])\r\n",
    "plt.yticks([-1, 0, 1])\r\n",
    "plt.ylim(-1, 1)\r\n",
    "plt.xlim(-4, 4)\r\n",
    "plt.show()"
   ],
   "outputs": [
    {
     "output_type": "display_data",
     "data": {
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ],
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"
     },
     "metadata": {}
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "source": [
    "# tanh函数比sigmoid好一点，但是好不了太多\r\n",
    "def tanh(x):\r\n",
    "    return (np.exp(x)-np.exp(-x))/(np.exp(x)+np.exp(-x))\r\n",
    "x =  np.linspace(-10.0,10,num=100)\r\n",
    "# 注意num参数不能为小数，因为是返回的数的个数，没有小数个数\r\n",
    "y = tanh(x)\r\n",
    "# 用seaborn画图\r\n",
    "sns.set()\r\n",
    "sns.lineplot(x,y)"
   ],
   "outputs": [
    {
     "output_type": "stream",
     "name": "stderr",
     "text": [
      "C:\\Users\\22459\\Miniconda3\\envs\\pytorch\\lib\\site-packages\\seaborn\\_decorators.py:36: FutureWarning: Pass the following variables as keyword args: x, y. From version 0.12, the only valid positional argument will be `data`, and passing other arguments without an explicit keyword will result in an error or misinterpretation.\n",
      "  warnings.warn(\n"
     ]
    },
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": [
       "<AxesSubplot:>"
      ]
     },
     "metadata": {},
     "execution_count": 19
    },
    {
     "output_type": "display_data",
     "data": {
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ],
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"
     },
     "metadata": {}
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "从上图可以看出，双曲正切函数和 Sigmoid 函数图像很相似，但是 Tanh 函数的范围为（-1,1），而 Sigmoid 函数的范围为 （0,1）。"
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "同 Sigmoid 类似，PyTorch 中也有两种方式实现 tanh："
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "source": [
    "x = torch.linspace(-10,10,10)\r\n",
    "\r\n",
    "output = torch.tanh(x)\r\n",
    "print(output)\r\n",
    "t = nn.Tanh()\r\n",
    "output = t(x)\r\n",
    "print(output)"
   ],
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "tensor([-1.0000, -1.0000, -1.0000, -0.9975, -0.8045,  0.8045,  0.9975,  1.0000,\n",
      "         1.0000,  1.0000])\n",
      "tensor([-1.0000, -1.0000, -1.0000, -0.9975, -0.8045,  0.8045,  0.9975,  1.0000,\n",
      "         1.0000,  1.0000])\n"
     ]
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "source": [
    "x = torch.linspace(-10,10,10)\r\n",
    "# 这个是函数\r\n",
    "print(torch.tanh(x))\r\n",
    "# 这个是对象\r\n",
    "print(nn.Tanh()(x))"
   ],
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "tensor([-1.0000, -1.0000, -1.0000, -0.9975, -0.8045,  0.8045,  0.9975,  1.0000,\n",
      "         1.0000,  1.0000])\n",
      "tensor([-1.0000, -1.0000, -1.0000, -0.9975, -0.8045,  0.8045,  0.9975,  1.0000,\n",
      "         1.0000,  1.0000])\n"
     ]
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "#### ReLU 函数"
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "双曲正切函数和 Sigmoid 函数相似，也存在着梯度消失现象。且由于解析式中存在幂运算，计算机需要消耗大量的时间成本。因此，为了解决梯度消失的问题，线性修正单元函数（Rectified Linear Units，简称ReLU）孕育而生。"
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "ReLU 函数是目前最常用的激活函数之一。公式如下所示："
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "$$f(x)=\n",
    "\\begin{cases}\n",
    "0& \\text{x $<$ 0}\\\\\n",
    "x& \\text{x $\\geq$ 0}\n",
    "\\end{cases}$$"
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "其中 $x$ 为常数。可以看到，当 $x<0$ 时，ReLU 全部取值为 0，梯度也为 0，减少了梯度的运算成本（这种现象称为硬饱和）。当 $x\\geq 0$ 时，ReLU 的取值为 $x$， 梯度始终为一个固定的值，进而缓解了梯度消失的问题。其函数图像如下所示："
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "source": [
    "def relu(x): return np.where(x >= 0, x, 0)\r\n",
    "# np.where(condition,x,y)\r\n",
    "# if condition: return x else return y\r\n",
    "\r\n",
    "y = np.linspace(-10, 10, 1000)\r\n",
    "plt.plot(y, relu(y), 'b')\r\n",
    "plt.grid(linestyle='--')\r\n",
    "\r\n",
    "plt.xticks([-3, -2, -1, 0, 1, 2, 3])\r\n",
    "plt.yticks([0, 1, 2, 3])\r\n",
    "plt.ylim(0, 3)\r\n",
    "plt.xlim(-3, 3)\r\n",
    "plt.show()"
   ],
   "outputs": [
    {
     "output_type": "display_data",
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     },
     "metadata": {}
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "source": [
    "def relu(x):\r\n",
    "    return np.where(x>0,x,0)\r\n",
    "x = np.linspace(-10,10,100)\r\n",
    "y = relu(x)\r\n",
    "print(x.shape,y.shape)\r\n",
    "sns.lineplot(x,y)"
   ],
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "(100,) (100,)\n"
     ]
    },
    {
     "output_type": "stream",
     "name": "stderr",
     "text": [
      "C:\\Users\\22459\\Miniconda3\\envs\\pytorch\\lib\\site-packages\\seaborn\\_decorators.py:36: FutureWarning: Pass the following variables as keyword args: x, y. From version 0.12, the only valid positional argument will be `data`, and passing other arguments without an explicit keyword will result in an error or misinterpretation.\n",
      "  warnings.warn(\n"
     ]
    },
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": [
       "<AxesSubplot:>"
      ]
     },
     "metadata": {},
     "execution_count": 35
    },
    {
     "output_type": "display_data",
     "data": {
      "text/plain": [
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My1ywyIkIAHCvSoHP96VA3qk9fh88iMOwzAiLnIigUqvx+b4U1NY3YPl0f7R3sJU6EmmhzUX+wQcfYOXKlfrIQkQS2XsyHTey7+HFyQPRXc5hWOamTUV+9uxZREVF6SsLEUng8o0iHPzpDsYO80agfxep45AOdC7ye/fuYf369ViyZIk+8xCRERWW1eCrA2nw6eKK2eM5DMtc2QghhC47vvzyy5g9ezby8vJw7tw5rFu3Tt/ZiMiAFEoVXv/sBxSV1eKTP42Fl7uT1JFIRzr9RePbb79F165dERgYiL179+p04JKSKqjV2v8MkctdUVRUqdMxDYm5tMNc2jFErn8dSENGbgX++JshkKlUOt2/Na2XvuiaTSazgYdH63+/0KnI4+LiUFRUhGnTpqG8vBw1NTV47733sGrVKl3ujoiM7NTVXJxOykPoUz4Y0ofDsMydTkX+73//u+nfe/fuxblz51jiRGbiTkEldhy+gcE+nRDxtK/UcUgPeB45kRWpqVNiY1QSXNrbYRGHYVmMNp/1HxkZicjISH1kISIDahyGlYbSCgXefOFxdHDiMCxLwWfkRFYi/qc7uHyzGM+P64u+3TtKHYf0iEVOZAWuZZXhu5O38cRAT0wY0V3qOKRnLHIiC3evSoHPY1LQxd0J86YO5DAsC8QiJ7JgDSo1Po9ORl19A5ZFcBiWpWKRE1mwvSfTcSOnHPOmDIQ3h2FZLBY5kYW6eL0I8efuYNzj3hjlx2FYloxFTmSBCkpr8K+4VPh27YBZz3IYlqVjkRNZGIVShY1RyZDZ2GBphB/sbPltbun4P0xkQYQQ2HHoOu4WVWFRuB86d2wvdSQyAhY5kQU5lZiHM0n5CBvtg4DeHlLHISNhkRNZiKz8Suw4dAN+vu4IH81hWNaERU5kAap/Hobl6mSHRWGDOQzLyrDIicycWghs3Z+GskoFlkX4w5XDsKwOi5zIzB38MQtXbhVj5rN90cebw7CsEYucyIylZZVh7w/pGDnIE+OHcxiWtWKRE5mpskoFvtiXzGFYxCInMkcNKjU270uGQqnG8ukBcLTnMCxrxiInMkPfnbiNWznlmDd1ILp1dpY6DkmMRU5kZi5cK8Sh89kY/3h3PDnYS+o4ZAJY5ERmJL+0Bv+KS4Nv1w54/tm+UschE8EiJzITinoVNkYlwbadDMsi/DkMi5rwkUBkBoQQ+O/315FbVI1F4YPh0dFR6khkQljkRGYg/scsnE3JR/jTvvD35TAsao5FTmTiMvIq8GVUEvx93RE22kfqOGSCWOREJqyqVolNUclwc3XAwrDBkPFNP9QKFjmRiVILga/2p+JelQJvvfgEh2HRA7HIiUzUgbNZSLxdglnj+6F/z05SxyETxiInMkEpmaWIPpWOJwd74dnHvaWOQyaORU5kYkor6vDFvhR09XDGvCkchkWPxiInMiH3h2EpVWosn+4PB/t2UkciM9CmkWkbNmzAwYMHAQBBQUF444039BKKyFp9c/wWbt+twJJpfujqwWFYpBmdn5EnJCTg9OnTiIqKQnR0NFJSUnD48GF9ZiOyKufSCnDkQg4mDO+OkYM4DIs0p/MzcrlcjpUrV8LevvGUqD59+iA3N1dvwYisSV5JNf598Br6eHMYFmlP5yLv169f078zMzMRFxeH3bt36yUUkTVR1KuwKSoZdu1kWDrNH7bt+Kcr0o6NEEK05Q5u3ryJxYsXY8WKFZg+fbq+chFZBSEE/t+uSzh5OQfvLAzEsAGeUkciM9SmP3ZevHgRL7/8MlatWoWQkBCt9i0pqYJarf3PELncFUVFlVrvZ2jMpR3manT8Ug5OXMpBxDO+6O7e/oHH5nppx1RzAbpnk8ls4OHh0uo2nYs8Ly8Py5cvx/r16xEYGKjr3RBZrYy8Cvzv6E0E9PZA6FM+UschM6ZzkW/duhUKhQLr1q1rum7WrFmYPXu2XoIRWbLGYVhJ6Ohsz2FY1GY6F/nq1auxevVqfWYhsgpqIbAlNhXl1fV4a85wuLS3kzoSmTn+eZzIyPYnZCIpvQSzx/eDb9cOUschC8AiJzKi5IwS7DuVgVF+Xhg7jMOwSD9Y5ERGUlpRhy9jUtGtszNenMxhWKQ/LHIiI2hQqbEpOhkNKjWWcRgW6RmLnMgIvj52C+m5Ffh98CAOwyK9Y5ETGdhPqQU4ejEHE0f0wBMD+c5N0j8WOZEB5RZXY9vBa+jr3RG/GddH6jhkoVjkRAZSV9+AjVFJsLeTYWkEh2GR4fCRRWQAQgj8J/468ktrsDjcD51cHaSORBaMRU5kAMcu3cVPqQWIeKY3Bvu4Sx2HLByLnEjPbueWY/fRmxjSxwMhgb2kjkNWgEVOpEeVNfXYHJ2MTq4OWBDKYVhkHCxyIj1RqxuHYVVU12PZdH8OwyKjYZET6UlsQiaSM0rxwsT+8OnCYVhkPCxyIj1ISi9BzOkMPOXfBUFDu0kdh6wMi5yojUrK67AlNhXecmf8bvIADsMio2ORE7WBsuH/hmEtnx4ABzsOwyLjY5ETtcHXx24iI68CL4UMgpe7k9RxyEqxyIl09GNKPo5duovJI3tg+AAOwyLpsMiJdHC3uBrb4q+hX/eOeC6Iw7BIWixyIi3VKhqwKSoJjnbtsGQah2GR9PgIJNJC4zCsa8gvrcGSaf4chkUmgUVOpIWjF3NwLq0QkWN6Y2CvTlLHIQLAIifS2O275fj62C081rczpo7iMCwyHSxyIg1U1NRj08/DsF4KHcRhWGRSWOREj6BWC2yJSUFljRLLpwfA2ZHDsMi0sMiJHiHmTAZSMsswZ1J/9OriKnUcohZY5EQPkXi7BDFnMjE6oAueGdJV6jhErWKREz1AcXkttsSmoLvcBXMmcRgWmS4WOVErlA1qbIpKhloILI/05zAsMmkscqJW7D56E5n5lXgpZDC8OnEYFpm2NhV5bGwsgoODMXHiROzcuVNfmYgklZCch+OX72LKyJ54vL9c6jhEj2Sr644FBQVYv3499u7dC3t7e8yaNQtPPvkk+vbtq898REZTq2jA53sTceBMBvr3cENkUG+pIxFpROciT0hIwKhRo+Dm5gYAmDx5MuLj4/GHP/xBX9laqFU04ExiLsrLaw12DF11yK1ARUWd1DFaYC7N1CoaEHsmA6WVCkwY0R2RY3pzGBaZDZ2LvLCwEHL5//3a6enpicTERI339/Bw0fqY0SdvYWtMitb7EWmiu6cLPpg7EoN83aWO0iq53DTPYWcu7ek7m85FLoRocZ02p2eVlFRBrW55Hw8TOMgTwwd6oaSkSqv9jKGTuzPKSquljtECc2nIxgZendqja5eOKCqqlDpNC3K5K3NpwVRzAbpnk8lsHvgEWOci9/LywoULF5ouFxYWwtPTsJ+SIrOxQQ9PVzia4G+8crkrnNqZ3nnGzEVk+XSuxKeeegpnz55FaWkpamtrcejQIYwZM0af2YiISANtekb+6quvYu7cuVAqlZgxYwaGDBmiz2xERKQBnYscAMLCwhAWFqavLEREpAMTfLWZiIi0wSInIjJzLHIiIjPXptfI20Im0/3Us7bsa0jMpR3m0g5zacdUcwG6ZXvYPjaitXf2EBGR2eBLK0REZo5FTkRk5ljkRERmjkVORGTmWORERGaORU5EZOZY5EREZo5FTkRk5ljkRERmTrK36Gvi008/hUwmw4oVKwAAFRUVeO2115CdnQ13d3d88sknzT43FGj8CLoPP/wQx48fh0wmw7vvvovhw4frNVdJSQnmz5/fdLmyshJlZWW4fPlys9vl5uYiJCQEPXv2BAB07twZW7du1WuWX4uOjsbHH38MDw8PAMDYsWPx6quvNruNJuuobxcvXsR7772HhoYGuLm54b333oO3t3ez2xhzvWJjY7F582YolUrMmzcPv/3tb5ttT0tLw+rVq1FVVYURI0bgnXfega2t4b9dNmzYgIMHDwIAgoKC8MYbb7TYvmfPHnTo0AEA8Pzzz7fIbghz585FSUlJ0xqsWbMGQ4cObdqekJCA999/HwqFAlOnTm3xmDOEb7/9Fjt27Gi6nJOTg2nTpuGvf/1r03XGXq+qqirMmjULn3/+Obp3767RuuTm5uL1119HSUkJfH198fHHH8PZ2Vm7AwsTVFFRId566y0xZMgQ8dlnnzVd/84774gvvvhCCCFEVFSUeOWVV1rse/DgQbFw4UKhUqlEenq6mDBhglAqlQbLqlKpxJw5c0RMTEyLbfHx8eIvf/mLwY7dmjVr1ojY2NiH3kaTddS3cePGibS0NCGEEN9++61YsmRJi9sYa73y8/PFuHHjRFlZmaiurhZhYWHi5s2bzW4TEhIiLl++LIQQ4q233hI7d+40eK4zZ86ImTNnCoVCIerr68XcuXPFoUOHmt1m8eLF4tKlSwbP8ktqtVqMHj36gd9HtbW1IigoSNy5c0colUoxf/58ceLECaNmvHHjhpg4caIoKSlpdr0x1+vKlSsiNDRU+Pn5iezsbI3XZdGiRWL//v1CCCE2bNggPvzwQ62PbZIvrRw9ehQ+Pj74/e9/3+z6EydONH2QRWhoKH744Qcolcpmtzl58iSCg4Mhk8ng6+uLbt26tXimrE979uxB+/btW/2AjaSkJNy4cQORkZGYO3curl+/brAcvzxmdHQ0wsPD8dprr6G8vLzFbTRZR32qr6/HK6+8goEDBwIABgwYgLy8vFazG2O9EhISMGrUKLi5ucHJyQmTJ09GfHx80/a7d++irq4Ojz32GAAgMjKy2XZDkcvlWLlyJezt7WFnZ4c+ffogNze32W2Sk5OxZcsWhIWFYc2aNVAoFAbPlZ6eDhsbGyxcuBDh4eHNngUDQGJiInr16oUePXrA1tYWYWFhRlmvX/rb3/6GV199Fe7u7s2uN+Z6ffPNN3j77bebPrtYk3VRKpU4f/48Jk+eDED3x5pJFnlERAQWLVqEdu3aNbu+sLCw6SUAW1tbuLi4oLS0tMVtfvkh0HK5HPn5+QbJqVKpsHnzZvz5z39udbuDgwMiIiKwd+9evPTSS1i+fDnq6+sNkuU+uVyOFStWYN++fejatSvWrFnT4jaarKM+2dvbY9q0aQAAtVqNDRs2YMKECS1uZ6z1+uXXDwCenp4oKCh44Ha5XN5su6H069ev6YdHZmYm4uLiEBQU1LS9uroagwYNwptvvomoqChUVFRg06ZNBs9VUVGBwMBAbNy4Edu2bcPu3btx5syZpu2PWk9DS0hIQF1dHaZOndrsemOv19q1azFixIimy5qsS1lZGVxcXJpestL1sSbpa+QHDx7E+++/3+y63r17Y9u2bRrfh0zW/GeRaGWY469vo42HZTx16hR8fX0xYMCAVve9/9o+0Ph65z/+8Q+kp6c3PTNtC03WbsGCBa0WZmvaskaa5qqvr8fKlSvR0NCAxYsXt9jXkOv1S609RmxsbDTebmg3b97E4sWL8eabb8LHx6fpemdnZ2zZsqXp8vz587Fq1SqDvx49bNgwDBs2DADg5OSEGTNm4OTJkxg9ejQA6ddr9+7dLX57B6Rbr/s0WRd9rZ2kRT516tQWP0UfxtPTE8XFxejSpQsaGhpQVVUFNze3Zrfx8vJCUVFR0+WioqJmz9D1mfHIkSMIDg5+4L7bt29HaGgoOnXqBKDxP01ffzBrLVdlZSW2bduGefPmPfR4mqyjPnMBjc+Oli5dCjc3N2zevBl2dnYtbmPI9folLy8vXLhwoenyr3+L8/LyQnFxcdPltj6GtHHx4kW8/PLLWLVqFUJCQppty83NRUJCAmbMmAHAcOvzaxcuXIBSqURgYGCrx/31ev16PQ2pvr4e58+fx7p161psk2q97tNkXdzd3VFVVQWVSoV27drp/FgzyZdWHiQoKAjR0dEAgLi4OIwYMaJFIYwZMwaxsbFQqVTIyspCZmYmAgICDJLnypUrzX6V+rXz58/ju+++AwCcO3cOarUavXv3NkgWoPHZ0ldffYWrV68CAHbs2IGJEye2uJ0m66hvr7/+Onr16oVPP/0U9vb2rd7GWOv11FNP4ezZsygtLUVtbS0OHTqEMWPGNG339vaGg4MDLl68CKDxTKBfbjeUvLw8LF++HB9//HGLEgcAR0dHfPTRR8jOzoYQAjt37mz1/1ffKisr8eGHH0KhUKCqqgpRUVHNjjt06FBkZGQgKysLKpUK+/fvN8p6AcD169fh4+MDJyenFtukWq/7NFkXOzs7jBgxAnFxcQDa8FjT4Y+zRvPZZ581O2ulrKxMLF68WAQHB4uZM2eK7OxsIYQQR44cEatWrRJCNP6Ffd26dSI4OFgEBweLU6dOGSzfkCFDRF1dXbPrdu3aJT755BMhROPZEfPmzRMhISEiMjKy6awNQzp//ryIiIgQU6ZMEUuWLBEVFRVCCCE++eQTsWvXLiHEg9fRUFJSUkT//v1FcHCwCA8PF+Hh4WLBggVCCOnWKyYmRoSEhIhJkyaJL7/8UgghxIIFC0RiYqIQQoi0tDTx3HPPiSlTpog//elPQqFQGCzLfe+++6547LHHmtYoPDxc7Nq1q1mu+Pj4ptwrV640Si4hhFi/fr2YMmWKmDRpkti2bZsQQojw8HCRn58vhBAiISFBhIWFiUmTJom1a9cKtVptlFwHDhwQf/zjH5tdJ/V6jRs3rul76kHrsmrVKnHkyBEhhBA5OTlizpw5YurUqWL+/Pni3r17Wh+TnxBERGTmzOqlFSIiaolFTkRk5ljkRERmjkVORGTmWORERGaORU5EZOZY5EREZo5FTkRk5v4/dgPV3x7FA0UAAAAASUVORK5CYII="
     },
     "metadata": {}
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "利用 PyTorch 中的 ReLU 函数处理输入数据："
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "source": [
    "x =  torch.linspace(-10,10,10)\r\n",
    "output = torch.relu(x)\r\n",
    "print(output)\r\n",
    "relu = nn.ReLU()\r\n",
    "output = relu(x)\r\n",
    "print(output)"
   ],
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "tensor([ 0.0000,  0.0000,  0.0000,  0.0000,  0.0000,  1.1111,  3.3333,  5.5556,\n",
      "         7.7778, 10.0000])\n",
      "tensor([ 0.0000,  0.0000,  0.0000,  0.0000,  0.0000,  1.1111,  3.3333,  5.5556,\n",
      "         7.7778, 10.0000])\n"
     ]
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "source": [
    "x =  torch.linspace(-10,10,10)\r\n",
    "print(torch.relu(x))\r\n",
    "print(nn.ReLU()(x))"
   ],
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "tensor([ 0.0000,  0.0000,  0.0000,  0.0000,  0.0000,  1.1111,  3.3333,  5.5556,\n",
      "         7.7778, 10.0000])\n",
      "tensor([ 0.0000,  0.0000,  0.0000,  0.0000,  0.0000,  1.1111,  3.3333,  5.5556,\n",
      "         7.7778, 10.0000])\n"
     ]
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "至此我们学习完了深度学习中常见的几种激活函数。当然，上一个试验中学到的 Softmax 函数也算一个激活函数，该函数主要应用于多分类模型的神经网络的最后一层。"
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "如果我们需要解决的是二分类问题，我们一般会将最后一层设置为 Sigmoid 函数层。因为，从 Sigmoid 函数图像可以看出，该函数的范围为 （0,1），这样可以很好的表示概率值。"
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "综上，考虑到每种激活函数的特性，我们得到了以下的规则："
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "- 如果在神经网络内部（隐含层）需要使用激活函数，一般会使用 ReLU 函数或者 ReLU 函数的改进来进行激活。\n",
    "- 如果是二分类问题，那么会在神经网络的最后一层加上一个 Sigmoid 函数层。\n",
    "- 如果是多分类问题，那么会在神经网络的最后一层加上一个 Softmax 函数层。"
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "### 神经网络的建立"
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "神经网络其实就是有很多各线性函数和非线性函数组成的复杂函数。至此，我们已经学习完了线性函数和非线性函数的定义方式。接下来，让我们根据这些知识点建立一个完整的神经网络模型。"
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "在利用 PyTorch 建立神经网络模型时，需要注意下面几个点："
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "- 自定的神经网络类必须继承 `nn.Module`。\n",
    "- 自定义类中需要实现 `__init__` 和 `forward` 函数。\n",
    "- `__init__` ： 定义网络的结构。\n",
    "-  `forward`：定义数据在模型中的传播路径。"
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "source": [
    "# 自定的神经网络类必须继承 `nn.Module`。\r\n",
    "class NeuralNet(nn.Module):\r\n",
    "    # init 函数主要用于定义，神经网络中有那些结果\r\n",
    "    def __init__(self, input_size, hidden_size):\r\n",
    "        super(NeuralNet, self).__init__()\r\n",
    "        self.linear1 = nn.Linear(input_size, hidden_size)\r\n",
    "        self.relu = nn.ReLU()\r\n",
    "        self.linear2 = nn.Linear(hidden_size, 1)\r\n",
    "        self.sigmoid = nn.Sigmoid()\r\n",
    "    # 将输出传入网络模型\r\n",
    "\r\n",
    "    def forward(self, x):\r\n",
    "        out = self.linear1(x)\r\n",
    "        out = self.relu(out)\r\n",
    "        out = self.linear2(out)\r\n",
    "        out = self.sigmoid(out)\r\n",
    "        return out\r\n",
    "\r\n",
    "\r\n",
    "# 测试代码\r\n",
    "model = NeuralNet(10, 20)\r\n",
    "model"
   ],
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": [
       "NeuralNet(\n",
       "  (linear1): Linear(in_features=10, out_features=20, bias=True)\n",
       "  (relu): ReLU()\n",
       "  (linear2): Linear(in_features=20, out_features=1, bias=True)\n",
       "  (sigmoid): Sigmoid()\n",
       ")"
      ]
     },
     "metadata": {},
     "execution_count": 39
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "source": [
    "import torch\r\n",
    "import torch.nn as nn\r\n",
    "import torch.nn.functional as F\r\n",
    "\r\n",
    "class MyModel(nn.Module):\r\n",
    "    def __init__(self,input_size, hidden_size):\r\n",
    "        super(MyModel,self).__init__()\r\n",
    "        self.linear1 = nn.Linear(in_features=input_size,out_features=hidden_size)\r\n",
    "        self.relu = nn.ReLU()\r\n",
    "        self.linear2 = nn.Linear(in_features=hidden_size,out_features=1)\r\n",
    "        self.sigmoid = nn.Sigmoid()\r\n",
    "\r\n",
    "    def forward(self,x):\r\n",
    "        x = self.linear1(x)\r\n",
    "        x = self.relu(x)\r\n",
    "        x = self.linear2(x)\r\n",
    "        x = self.sigmoid(x)\r\n",
    "        return x\r\n",
    "model = MyModel(1,1)\r\n",
    "model"
   ],
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": [
       "MyModel(\n",
       "  (linear1): Linear(in_features=1, out_features=1, bias=True)\n",
       "  (relu): ReLU()\n",
       "  (linear2): Linear(in_features=1, out_features=1, bias=True)\n",
       "  (sigmoid): Sigmoid()\n",
       ")"
      ]
     },
     "metadata": {},
     "execution_count": 40
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "从结果可以看出，我们建立的神经网络结构为：连接层（线性函数层）-> ReLU 层 -> 连接层 -> Sigmoid 函数层。"
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "如果中间有多个 ReLU 函数层，那么按照上面的思路，我们就需要定义 relu1，relu2 ... \r\n",
    "我觉得这是没有必要的,因为激活函数没有参数,一个relu可以多次使用啊"
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "当然在定义激活层时，我们可以将其放在 `forward()` 函数中，这样可以减少变量的定义，如下："
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "source": [
    "class NeuralNet(nn.Module):\r\n",
    "    def __init__(self, input_size, hidden_size):\r\n",
    "        super(NeuralNet, self).__init__()\r\n",
    "        self.linear1 = nn.Linear(input_size, hidden_size)\r\n",
    "        self.linear2 = nn.Linear(hidden_size, 1)\r\n",
    "\r\n",
    "    # 将激活函数层直接放到 forward 中\r\n",
    "    def forward(self, x):\r\n",
    "        out = torch.relu(self.linear1(x))\r\n",
    "        out = torch.sigmoid(self.linear2(out))\r\n",
    "        return out\r\n",
    "\r\n",
    "\r\n",
    "# 测试代码\r\n",
    "model = NeuralNet(10, 20)\r\n",
    "model"
   ],
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": [
       "NeuralNet(\n",
       "  (linear1): Linear(in_features=10, out_features=20, bias=True)\n",
       "  (linear2): Linear(in_features=20, out_features=1, bias=True)\n",
       ")"
      ]
     },
     "metadata": {},
     "execution_count": 43
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "source": [
    "class NeuralNet(nn.Module):\r\n",
    "    def __init__(self, input_size, hidden_size):\r\n",
    "        super(NeuralNet, self).__init__()\r\n",
    "        self.linear1 = nn.Linear(input_size, hidden_size)\r\n",
    "        self.linear2 = nn.Linear(hidden_size, 1)\r\n",
    "\r\n",
    "    # 将激活函数层直接放到 forward 中\r\n",
    "    def forward(self, x):\r\n",
    "        out = torch.relu(self.linear1(x))\r\n",
    "        out = torch.sigmoid(self.linear2(out))\r\n",
    "        return out\r\n",
    "\r\n",
    "\r\n",
    "# 测试代码\r\n",
    "model = NeuralNet(10, 20)\r\n",
    "model"
   ],
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": [
       "NeuralNet(\n",
       "  (linear1): Linear(in_features=10, out_features=20, bias=True)\n",
       "  (linear2): Linear(in_features=20, out_features=1, bias=True)\n",
       ")"
      ]
     },
     "metadata": {},
     "execution_count": 46
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "当然，这样就无法输出 激活函数层的结构了。因为激活函数层被放在了 `forward()` 中，只有调用 forward() 函数时（即传入数据时），计算机才知道还需要进行激活处理。"
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "### 实验总结"
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "本实验首先讲述了激活函数的主要形式以及用处，然后利用 PyTorch 对每种激活函数进行了实现与应用，最后利用前面所学知识建立了一个简单的神经网络模型。"
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "<hr><div style=\"color: #999; font-size: 12px;\"><i class=\"fa fa-copyright\" aria-hidden=\"true\"> 本课程内容版权归蓝桥云课所有，禁止转载、下载及非法传播。</i></div>"
   ],
   "metadata": {}
  }
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